We are studying indifference curves in economics, and these are applied to marginal utility calculations, thus some mathematical background would be appreciated. Do convex curves have a negative or positive dy/dx? Would you kindly explain the theorem please?

Is it correct to deduce the tangent of f(x) = 5x^3 + 5x^2 + x + 1 at x = 0.5 to be y = 9.75x - 1.5? If yes, could you show the workings? I have this software named Graph v4.4 (http://www.padowan.dk), which deduced the tangent above, and, according to my knowledge the tangent would be calculated by d...

In economy A there are two types of labour (say, skilled and unskilled). The economy produces two goods (x and y) which can be produced either by skilled labour or unskilled one. Skilled labour can produce either 400 units of y or 200 units of x (or any linear combination of the two). Unskilled labo...

I am trying to find the point of intersection of the following graphs, and, wondering whether it may help me with the logic behind a graphing dilemma that I have with an economic problem, because somehow I am thinking that the point of intersection for the production possibility curve represents som...

I am trying to figure out the function of a graph that I sketched, and, I think I am getting it wrong. Please include the workings and sources of reference so I can look up similar problems in the future, please. What is the gradient anyway? A copy of the sketched graph is available at https://skydr...